Question

A pair of dice is thrown $4$ times. If getting 'a total of $9$' in a single throw is considered as a success then find the probability of getting 'a total of $9$' thrice.

Answer 1

P=probability of getting 'a total of $9$'$=\frac{4}{36}=\frac{1}{9}$
$\therefore$ $q=1-\frac{1}{9}=\frac{8}{9}$
$r=3,n=4$
$\therefore$ $P(r=3){=}^4{\text{C}}_3{p}^{3}q=4{\left(\frac{1}{9}\right)}^3.\frac{8}{9}=\frac{32}{6561}$